Case $V\to \infty$

In this case, $\kappa \to \infty$ and

$$= \tan \left(k\frac{a-L}{2}\right)\leadsto k\frac{L-a}{2}=n\pi,\quad n=1,2,3,...,$$ 0 (158)

where $(L-a)/2$ is the length of the two infinite potential wells that are completely separated by the infinitely high barrier. The wave functions in the two wells and the energies are just the ones that we have calculated for an infinite potential well.